Zen is not anti-rational. It is supra-rational which is very different. But the West being intrinsically dualistic and fascinated by Paradox and Absurdity is blind to non-duality. Supra-rational is synonymous with the nondual (meaning actually non-cardinal, i.e. Not One! Not Two! Not Many!, which is the same as the meaning of Emptiness based on the Tetralemma (A, Not A, Both or Neither). See Loy’s Book Nonduality, except he accepts Monism as Nondual which is a problem with his presentation. As I have explained in my other answers viz Buddhism, DzogChen, Taoism etc. Zen is fundamentally misunderstood in the West as being Paradoxical. Nothing could be further from the truth and in fact exactly the opposite is true. If we look at Plato’s Divided Line we see it has two limits Contradiction, Paradox, Absurdity on the one hand and Supra-rationality on the other. This is like the difference in Quantum Mechanics between Entanglement and Superposition. Supra-Rational is like Superposition. It means that two things are simultaneously true without interfering or mixing. In Contradiction, Paradox and Absurdity there is mixture. Very few Zen Koans are about Mixture. Many are about the Pure States of SupraRationality in which opposites are true simultaneously without reference to each other or mixture because there is a barrier between the two states that prevent mixture. If you can see that state of simultaneous truth, or falsehood then that is an indicator of the nondual state of emptiness or in Taoism Void. The association of Zen with anti-rationalism is a form of Orientalism in which the West sees everything foreign in its own image. It takes a lot of time and energy to get past this misconception. That is because there are very few examples of supra-rationality in our culture, and it truly is culture shock to realize that there are states for which there are few precedents in our culture to be able to relate to them, however if we go back to the core of the Western worldview which is the Divided Line of Plato we see that the other limit of that line associated with Nous of the Numinous is the Greek expression of the supra-rational. Thus the precedents are there but they are well hidden.